SVC Damping Controller Design Based on Firefly ... - IEEE Xplore

2013 IEEE Conference on Clean Energy and Technology (CEAT)

SVC Damping Controller Design Based on Firefly Optimization Algorithm in Multi Machine Power System Naz Niamul Islam, M A Hannan, Hussain Shareef and Azah Mohamed Department of Electrical, Electronic & System Engineering University Kebangsaan Malaysia Bangi, Selangor, Malaysia [email protected], [email protected], [email protected],[email protected] lack of proper damping [2]. In order to get enough damping over local as well as inter-area modes of low frequency oscillation, Static VAR Compensator (SVC) have become popular as a shunt FACTS device [3-5, 14-15]. SVC is employed in transmission line and contributes to attain enough damping especially for inter-area modes as well as local modes[3]. The total effectiveness of SVC during power system oscillation relies on how properly the SVC is designed.. Conventional lead-lag controller is the most used structure as a supplementary SVC controller due to its simple design, easy to implementation [6]. Accurately, tuning parameters is the design problem of SVC. Meta heuristic optimization method is generally employed to determine optimum value of FACTS (SVC) controller parameters [4, 7-12]. In [5], a real coded genetic optimization algorithm(RCGA) was used for optimum controller parameter determination. Another popular algorithm known as particle swarm optimization (PSO) was also used for the best parameter determination in [7, 8]. To assess the application of PSO with genetic algorithm (GA) for tuning of FACTS controller, a comprehensive analysis was carried out in [9]. More recently, another optimization named as bacteria foraging algorithm has been used for SVC supplementary controller design [4]. In this study, a new optimization technique called Firefly Algorithm (FA) is proposed for optimum design of SVC in a multi machine system to suppress growing inter-area mode oscillation as well as local mode oscillation. SVC parameters are tuned effectively with FA so that damping is quite enough to suppress growing oscillations. Selection of SVC parameters is transformed to optimization problem after subjected to a disturbance and FA is then employed to decrease the formulated cost function in order to improve damping and as a result suppressed oscillations. Thus ensuring overall system stability, security and finally reliability.

Abstract— Power system stability is a great concern in today's interconnected power system especially when the system is subjected to a fault. These faults occasionally lead to Low Frequency Oscillation (LFO). Therefore, Shunt Flexible AC Transmission System (FACTS) devices for example, SVC are employed to provide damping to attain system stability. The performance of SVC is totally dependent on proper tuning of its controller and usually heuristic optimization techniques are used to search the best controller parameters. In this paper, a popular metaheuristic optimization technique known as Firefly Algorithm (FA) is presented for optimal design of SVC controller in multi machine power system. In the simulation, the linearized model of power system and conventional lead-lag controller as SVC damping controller are used. The performance of obtained results using Firefly Algorithm (FA) is compared with the results obtained from Particle Swarm Optimization (PSO) Algorithm. The comparison of attained results show that FA can find more optimal parameter values of SVC damping controller and subsequently enhance power system stability. Index Terms— FACTS, SVC, Damping Controller, Multi Machine Power System, Firefly Algorithm (FA), Optimization

I. INTRODUCTION The stability of today's power system is a very significant deals of attention. Over the years, the demand in electricity has increased dramatically. To meet the growing demand, power system become interconnected through long transmission line to transfer large amount of power from one load point to another. In order to transfer huge power it is emerged essential to make use of the existing transmission-line instead of new line installation considering extra cost, environmental issues, time, etc. The stability limit of transmission line prevents full utilization of existing line. Therefore sufficient damping over low frequency oscillation (LFO) of power system can extend stability limit as well as ensure secure and reliable operation of power system[1] Oscillation in power system can be found in the frequency range of 0.1 - 3 Hz [1, 2]. This range of oscillation in power system is known as low frequency oscillation (LFO). Oscillatory mode of frequency above 1 Hz is called local mode of oscillation and oscillation between 0.1 - 1 Hz is called inter area oscillation mode. The inter-area mode is very crucial than the local mode and cause the system instability very easily with

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II. FIREFLY ALGORITHM (FA) Firefly optimization technique is a meta heuristic and nature-inspired optimization method that comprises firefly’s social behavior. In nature, they produce rhythmic fluorescent flashes from their lower abdomen to communicate with other mates. The pattern of light emission determines their

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2013 IEEE Conference on Clean Energy and Technology (CEAT)

light. So the attractiveness of a firefly can be determined using Eq. 2.

communication to attract potential prey and to attract partner mates. This natural characteristic was mimicked into optimization search algorithm by Yang [13] at Cambridge University in 2009. For simplicity, the following initial assumptions are taken for this algorithm development[13] 1. Every firefly in their population is assumed to be unisex. That means any firefly can be attracted to any other firefly without considering their sex. 2. Firefly’s brightness is determined from objective function. 3. Attractiveness of a firefly varies proportionally to their brightness. So a brighter firefly will attract comparatively less brighter firefly. But their brightness decrease as increasing the distance between them. Based on the initial assumptions, the fundamental work flows of FA are epitomized as the following block diagram Fig. 1.

2

β = β 0 e −γ ⋅ r (2) Where β 0 is the firefly attractiveness at r = 0 and γ is the absorption coefficient. In this investigation, both β 0 and γ are set to 1. If a firefly i is apart from a firefly j then the distance between two fireflies is calculated using Eq. 3. d 2 (3) ¦ ( xi, k − x j , k ) k =1 If one firefly i is tempted to a brighter firefly j then firefly i will use Eq. 4 for its movement. 1 −γ ⋅r 2 xi = xi + β 0 e ij ( x j − xi ) + α (rand − ) (4) 2 In Eq. 4, the first term is firefly’s recent position, second term is calculated using firefly’s brightness and third term determines randomization. Here α is the randomization parameter. rij = xi − x j =

III. MULTI MACHINE TEST SYSTEM In this study, a four machine two area power system is taken into account for the design of SVC damping controller presented in Fig. 2 by using power system toolbox [2]. In each area, there are two generator units and all generators are equipped with identical turbines, governor and excitation controls. Two loads are connected at Bus 4 and 14. Shunt FACTS device, SVC is placed with its supplementary controller in the middle of the tie line at bus 101. The model simulates the basic power system electromechanical swings. These types of swings are tempted to grow in interconnected power system systems only. In this system, three modes of electromechanical oscillation exist. Generators of first area oscillate with generators of second area. This oscillation is known as inter-area mode. The whole system can easily goes uncontrollable state with this type of oscillatory mode. The other two modes are associated with two local modes of individual generators areas.

Fig. 1. Block diagram of FA.

In FA, the first position of a firefly is generated by using Eq. 1 x ij = rand ⋅ (up j − low j ) + low j (1)

Here, rand is uniformly distributed pseudorandom number. up and low are the row vectors of upper limits and lower limits for optimizing parameters respectively in search space. In a visible range of one firefly, the attractiveness is directly proportional to its brightness. But brightness of a firefly decrease with the increase of distance from the source of

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Fig. 2. Single line diagram of four-machine two-area power system

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2013 IEEE Conference on Clean Energy and Technology (CEAT)

IV. PROBLEM FORMULATION

C. Objective Function In a disturbed power system, the damping ratios of eigenvalues obtained from linearized time invariant model determine system stability. An unstable system can become stable if the damping ratios are forced to shift toward its maximum value considering all boundary conditions. The highest value of damping ratio is 1. So the objective function can be formulated as comprehensive damping index (CDI) [6], which will be minimized

A. Power System Model In this study, a set of nonlinear differential equations are used to model the power system: x = f ( x, u )

(5)

Where x = [ Δδ , Δω , E q' ,ψ d" , E d' ,ψ q" ] and u are the vectors of state variables and input variables respectively. For this study, as SVC is used as damping controller, u is the output signal of SVC. In state variables vector, Δδ is rotor angle, Δω is speed deviation, E d' and E d' are stator voltage’s d-q quantities. Stator flux’s d-q quantities are ψ d" andψ q" . For small signal analysis

n

CDI =

Minimize:

¦ (1 − ξ )

(9)

i =1

Subject to K min ≤ K ≤ K max

and SVC design, the power system is linearized to a single linear time invariant (LTI) model as shown in Eq. 6.

Tw,min ≤ Tw ≤ Tw,max

Δx = AΔx + BΔu (6) Δy = CΔx + DΔu Where ǡǡƒ† are the state matrix, input matrix, output matrix and feed-forward matrix of the system respectively. The eigenvalues, λ = σ ± jω of the total system are evaluated from Eq. 6. The stability of the overall power system is evaluated based on the examination of eigenvalue location in splane. In other term, damping ratio ሺ ξ ሻ determines the system stability and can be calculated from Eq. 7. −σ i ξ= (7) 2 2 σ +ω For system stability, all damping ratios must meet Eq. 8

T2,min ≤ T2 ≤ T2,max

T1,min ≤ T1 ≤ T1,max

The goal of the optimization is to increase the damping ratios of eigenvalues towards unity value and thus minimize the CDI as much as possible. For all time constant, the lower and upper limits set to 0.01 and 2 seconds respectively. The range of gain constant is from 0.01 to 100. The minimum damping ratio ( ξ 0 ) for this study is considered to 0.1. V. SIMULATION RESULT To evaluate the effectiveness of the firefly optimization algorithm, simulation is carried out in linearized model as well as non-linear model of study system. The single-line outline of the multi-machine power system is presented in Fig. 2. For both FA and PSO, the total generation, population size, problem dimension are set to 350, 50, 4 respectively. The comparative convergence curve to minimize formulated objective function using linearized model is shown in Fig.4.

ξ ≥ ξ0 (8) Where, ξ 0  is the minimum damping ratio required for system stability. B. SVC Controller In this study, conventional lead-lag structure is used as the supplementary controller for SVC shown in Fig. 3. [2]. It is comprised of a gain block, a washout block and one stage leadlag block. K is the gain of gain block, where Tw is the time constant of washout block. For one stage lead-lag block, the time constants are T1 and T2. The input of the SVC supplementary damping controller is line voltage at the bus where it is placed.

16 FA PSO

15 14

CDI

13 12 11 10 9 0

50

100

150 200 Generation

250

300

350

Fig. 4. Convergence curve for FA and PSO

Fig. 3. Block diagram for supplementary controller of SVC

From proposed optimization technique, the obtained tuned parameters for the SVC supplementary controller are listed at

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Table I. and PSO based optimized parameters are shown in Table II.

1.005 FA Optimized PSO Optimized Without Controller

1.004

TABLE I. OPTIMAL PARAMETERS OF SVC SUPPLEMENTARY CONTROLLER BY FIREFLY ALGORITHM

T1 1.4513

Tw 1.0642

Rotor Speed (G2)

K 12.3734

1.003

T2 0.0681

TABLE II. OPTIMAL PARAMETERS OF SVC SUPPLEMENTARY CONTROLLER BY PARTICLE SWARM OPTIMIZATION

K 27.6426

T1 1.2371

Tw 0.7843

1.002 1.001 1

T2 0.3124

0.999 0.998 0

For the non-linear model simulation, a 100 ms three phase disturbance is implemented at Bus 3. The disturbance at Bus 3 has been removed after 150ms and at remote end Bus 101 is cleared after 200ms. Due to the three-phase fault, a inter-area mode of oscillations is tempted to grow but suppressed very quickly because of the SVC damping controller at Bus 101. The rotor speed response for all the four generators are shown in Fig. 5-8 with comparison of results obtained from PSO algorithm and also the system without any controller. In the study system, the nearby generators of the fault area are G1 and G2. According to the Fig. 5-8, FA based controller provided much better damping than the PSO based controller over the growing oscillations in both of the generators (G1, G2). On the other hand, remote generators G3, G4 are also affected due the three phase fault as shown Fig. 6-7. But both of the generators G3, G4 attained stability faster for FA based controller compared with PSO based controller. For all the affected generators, obtained results show that FA based controller performance is much better than PSO based controller.

2

4

6

8

10

Time

Fig. 6. Rotor Speed response for Generator 2

1.005 FA Optimized PSO Optimized Without Controller

1.004

Rotor Speed(G3)

1.003 1.002 1.001 1 0.999 0.998 0.997 0

2

4

6

8

10

Time 1.005

Fig. 7. Rotor Speed response for Generator 3

FA Optimized PSO Optimized Without Controller

1.004

1.005 FA Optimized PSO Optimized Without Controller

1.004

1.002 1.003

1.001

Rotor Speed (G4)

Rotor Speed (G1)

1.003

1 0.999 0.998 0

1.002 1.001 1 0.999

2

4

6

8

10

Time

0.998 0.997 0

Fig. 5. Rotor Speed response for Generator 1

2

4

6

Time

Fig. 8. Rotor Speed response for Generator 4

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VI. CONCLUSION

[13] X.-S. Yang, “Firefly algorithms for multimodal optimization,” in Stochastic algorithms: foundations and applications, ed: Springer, 2009, pp. 169-178. [14] M.A. Hannan, A. Mohamed, A. Hussain, M. Al-Dabbagh, “Power Quality Analysis of STATCOM using Dynamic Phasor Modeling,” International Journal of Electric Power System Research, vol. 79, pp. 993 - 999., 2011 [15] M.A. Hannan, K.W. Chan, “Transient Analysis of FACTS and Custom Power Devices using Phasor Dynamics,” Journal of Applied Science, vol. 6, pp.1074 – 1081, 2006

This paper suggests a new metaheuristic optimization technique named as FA for optimum tuning of SVC damping controller to provide sufficient damping suppressing swings of power system. The design problem of SVC controller is formulated as an optimization problem and then FA is used to find for best optimum parameter values. The obtained results validate the superiority of the FA over PSO in SVC controller parameter tuning. Although only SVC is simulated in this proposed FA, other FACTS device such as TCSC can also be modeled for optimal damping controller design REFERENCES [1] P. Kundur, “Power system stability and control,” Tata McGrawHill Education” Tata McGraw-Hill Education, 1994. [2] G. Rogers, “Power Systems Oscillations,” Kluwer Academic, 2000. [3] N. G. Hingorani, L. Gyugyi, and M. El-Hawary, “Understanding FACTS: concepts and technology of flexible AC transmission systems,” vol. 1, IEEE press, New York, 2000. [4] S. Abd-Elazim and E. Ali, “Bacteria Foraging Optimization Algorithm based SVC damping controller design for power system stability enhancement,” International Journal of Electrical Power & Energy Systems, vol. 43, pp. 933-940, 2012. [5] M. Abido and Y. Abdel-Magid, “Coordinated design of a PSS and an SVC-based controller to enhance power system stability,” International Journal of Electrical Power & Energy Systems, vol. 25, pp. 695-704, 2003. [6] L.-J. Cai and I. Erlich, “Simultaneous coordinated tuning of PSS and FACTS damping controllers in large power systems,” Power Systems, IEEE Transactions on, vol. 20, pp. 294-300, 2005. [7] D. Mondal, A. Chakrabarti, and A. Sengupta, “PSO based location and parameter setting of advance SVC controller with comparison to GA in mitigating small signal oscillations,” in Energy, Automation, and Signal (ICEAS), 2011 International Conference on, 2011, pp. 1-6. [8] D. Mondal, A. Chakrabarti, and A. Sengupta, “Optimal placement and parameter setting of SVC and TCSC using PSO to mitigate small signal stability problem,” International Journal of Electrical Power & Energy Systems, vol. 42, pp. 334-340, 2012. [9] S. Panda and N. P. Padhy, “Comparison of particle swarm optimization and genetic algorithm for FACTS-based controller design,” Applied soft computing, vol. 8, pp. 1418-1427, 2008. [10] H. Shayeghi, A. Safari, and H. Shayanfar, “PSS and TCSC damping controller coordinated design using PSO in multimachine power system,” Energy Conversion and Management, vol. 51, pp. 2930-2937, 2010. [11] S. Abd-Elazim and E. Ali, “Coordinated design of PSSs and SVC via bacteria foraging optimization algorithm in a multimachine power system,” International Journal of Electrical Power & Energy Systems, 2012. [12] M. Eslami, H. Shareef, and M. Khajehzadeh, “Optimal design of damping controllers using a new hybrid artificial bee colony algorithm,” International Journal of Electrical Power & Energy Systems, vol. 52, pp. 42-54, 2013.

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